Let $\theta \in \left( {0,{\pi \over 2}} \right)$. If the system of linear equations $(1 + {\cos ^2}\theta )x + {\sin ^2}\theta y + 4\sin 3\,\theta z = 0$, ${\cos ^2}\theta x + (1 + {\sin ^2}\theta )y + 4\sin 3\,\theta z = 0$, ${\cos ^2}\theta x + {\sin ^2}\theta y + (1 + 4\sin 3\,\theta )z = 0,$ has a non-trivial solution, then the value of $\theta$ is :